Mathematics Tes...

If $f\left(x\right)=2\sin x,g\left(x\right)={\cos }^{2}x$, then$\left(f+g\right)\left(\frac{\mathrm{\pi }}{3}\right)=?$

Which one of the following is correct in respect of the function f : R → R⁺ defined as f(x) = |x+1|?

Consider the following statements:

1. Every zero matrix is a square matrix.

2. A matrix has a numerical value.

3. A unit matrix is a diagonal matrix.

Which of the above statements is/are correct?

Which of the following statements is/are true:

I. If A is a set then ϕ is a subset of A.

II. If B = {x ∈ N : x < 1} then B is an empty set.

What is the order of the product \([\mathrm{x} \mathrm{y} \mathrm{z}]\left[\begin{array}{lll}\mathrm{a} & \mathrm{h} & \mathrm{g} \\ \mathrm{h} & \mathrm{b} & \mathrm{f} \\ \mathrm{g} & \mathrm{f} & \mathrm{c}\end{array}\right]\left[\begin{array}{l}\mathrm{x} \\ \mathrm{y} \\ \mathrm{z}\end{array}\right] ?\)

Suppose f : R → R is defined by \(f(x)=\frac{x^{2}}{1+x^{2}}\). What is the range of the function?

Solve the following Linear Programming Problems graphically:

Minimise \(\mathrm{Z}=-3 \mathrm{x}+4 \mathrm{y}\), subject to \(x+2 y \leq 8,3 x+2 y \leq 12, x \geq 0, y \geq 0\)

The value of \(\sin ^{-1} \sin \left(\frac{33 \pi}{5}\right)\) is?

\(\int_{0}^{\frac{\pi}{2}}|\sin x-\cos x| d x\) is equal to: